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Brief Report: Epidemiology and Prevention

Illustration of a Measure to Combine Viral Suppression and Viral Rebound in Studies of HIV Therapy

Edwards, Jessie K. PhD*; Cole, Stephen R. PhD*; Adimora, Adaora MD, MPH; Fine, Jason PhD; Martin, Jeff MD, MPH§; Eron, Joseph MD

Author Information
JAIDS Journal of Acquired Immune Deficiency Syndromes: February 1, 2015 - Volume 68 - Issue 2 - p 241-244
doi: 10.1097/QAI.0000000000000423

Abstract

INTRODUCTION

Plasma HIV-1 RNA (henceforth, viral load) is an important biomarker to monitor infection and to assess the prognosis of patients with HIV. Clinicians use measurements of viral load together with CD4 cell count, symptoms, and AIDS-defining illnesses to inform treatment decisions and assess the efficacy of a given antiretroviral treatment regimen.1

Viral load is also an important measure for researchers wishing to describe effects of a treatment over time or to compare effects of treatment regimens.2 Perhaps, the most commonly used end point to compare the efficacy of treatment plans is the time to “virologic failure.”3–7 The time to virologic failure for patients whose viral load is not suppressed by a predetermined time during the study period is often set to that predetermined time5,6 or time zero.8 In addition, studies using virologic failure as an end point often ignore viremia before suppression by measuring the time to virologic failure as the time from study onset to viral rebound.7

Gouskova et al9 formalized an alternative end point based on multistate methods,10 which uses information on time to both viral load suppression and rebound to estimate the probability of being suppressed as a function of time from study onset. Here, we provide an illustrative example in which we estimate this measure to compare the efficacy of 2 treatment regimens in a randomized trial.

METHODS

We compare this alternative end point between treatment arms in publicly available de-identified data from the AIDS Clinical Trials Group A5095 trial6 conducted between March 2001 and March 2005. Briefly, 1125 therapy-naive patients infected with HIV-1 were randomized to 1 of 3 arms: a triple-nucleoside regimen (zidovudine, lamivudine, and abacavir), a 3-drug standard of care regimen with efavirenz (zidovudine, lamivudine, and efavirenz), or a 4-drug regimen with efavirenz (zidovudine, lamivudine, abacavir, and efavirenz). We limit the analysis to patients randomized to the 3- and 4-drug efavirenz-containing regimens (as did Gulick et al6) because the triple-nucleoside group was discontinued. Data for 761 of the 765 patients in the 3- and 4-drug arms were available in the public-use data set. Treatment was initiated at randomization. Study visits were conducted at weeks 2, 4, 8, 12, 16, 20, 24, and then every 8 weeks, and viral load was measured at each study visit. Here, we perform an intent-to-treat analysis in which we estimate the effect of being randomized to a specific treatment regimen, rather than the effect of the actual treatment received.

Patients were followed from randomization until viral rebound or censoring at the time of death, loss to follow-up, or 1012 days. A patient is considered lost to follow-up if his last visit was before day 1012 and he had not yet experienced viral rebound or death. Following Gulick et al,6 a patient's viral load was “suppressed” if it was below 200 copies per milliliter, and a patient was considered to have experienced viral rebound if his viral load rose above 200 copies per milliliter after dropping below this threshold. Alternative thresholds for suppression and rebound could be chosen. We assume that viral load was unsuppressed until the first viral load measurement in which viral load was suppressed (and likewise for viral rebound).

To summarize treatment effects, we compare the mean time patients spend in a state of viral suppression in each trial arm.9 We define a patient to be in a “state of viral suppression” after initial viral suppression and before first viral rebound. To estimate this outcome measure for 1 treatment arm, we begin by estimating the probability of being in a state of suppression at each time point. Specifically, being suppressed at time t requires that a patient has already experienced viral suppression by time t but not yet experienced viral rebound. Accordingly, the probability of being in a state of suppression can be denoted by G(t) and estimated for each treatment arm x as

where

is the product-limit estimator of the Kaplan–Meier survivor function for rebound for treatment arm X = x and

is the survivor function for initial viral suppression for that treatment arm. Note that

will always be greater than

because, by definition, a patient's viral load cannot rebound before it is suppressed below the threshold value. The quantity

has the intuitive interpretation as the proportion of patients in treatment arm x who have not yet rebounded, excluding those who have not yet initially suppressed. This measure can be summarized as the τ-restricted mean time spent in a state of suppression (before rebound) by integrating

over the study period τ. Because the survivor functions can change at most once per day, the mean time suppressed over the 1012-day follow-up period for treatment arm x can be calculated as the Riemann sum

. The components of this measure for each arm can be seen in Figure 1.

F1-19
FIGURE 1:
Illustration of the survival curve for suppression (solid line), the survival curve for rebound (dashed line), and the restricted mean time spent in a state of for 380 patients in the 3-drug arm (A) and 381 patients n the 4-drug arm (B) of the ACTG A5095 trial over 1012 days of follow-up. The survival curves for initial viral suppression,
, and viral rebound,
, were estimated using the Kaplan Meier product-limit estimator of the survivor function. Details are provided in the Appendix 1 (see Supplemental Digital Content, https://links.lww.com/QAI/A591). The restricted mean number of days spent in a state of suppression (ie, time after initial suppression and before viral rebound) over the 1012-day follow-up period for each arm was estimated as
, where
.

The difference in mean time spent in a state of suppression can be compared between treatment regimens, with inference based on the closed-form equation for the variance presented in Appendix 1 (see Supplemental Digital Content,https://links.lww.com/QAI/A591) or a nonparametric bootstrap. Additional technical details and SAS computer code are provided in Appendices 1 and 2 (see Supplemental Digital Content,https://links.lww.com/QAI/A591).

RESULTS

The 761 participants were 81% male, had a mean age of 37, and were predominantly white (41%) or black (35%). The prevalence of hepatitis C virus was 10% and the prevalence of hepatitis B virus was 3%. Demographic characteristics were similar between the 380 patients in the 3-drug arm and the 381 patients in the 4-drug arm.

Over the 1012 days of follow-up, 12 patients died (8 in the 3-drug arm and 4 in the 4-drug arm) and 236 patients became lost to follow-up (111 in the 3-drug arm and 125 in the 4-drug arm). Over the course of follow-up, 356 patients in the 3-drug arm (93.7%) and 354 patients in the 4-drug arm (92.9%) responded to treatment by suppressing their HIV-1 RNA viral load below 200 copies per milliliter at 1 or more time points. The median time from randomization to initial viral load suppression was 56 days in both groups. During the course of follow-up, 121 patients in the 3-drug arm and 112 patients in the 4-drug arm experienced viral rebound after initial viral suppression. The probability of being in a state of suppression before rebound at each time during follow-up, Gx(t), can be seen for both arms in Figure 2. Over the 1012-day follow-up period, the average number of days suppressed before rebound was 644 in the 3-drug arm and 686 in the 4-drug arm, for a difference of 42 days in favor of the 4-drug regimen (95% confidence interval: −11 to 96).

F2-19
FIGURE 2:
Probability of being in a state of suppression before viral rebound, G x(t), for 380 patients in the 3-drug arm and 381 patients in the 4-drug arm of the ACTG A5095 trial over 1012 days of follow-up.

DISCUSSION

Using the proposed end point, we have demonstrated that the 4-drug regimen conferred a slight benefit over the 3-drug regimen in terms of number of days spent in a state of viral suppression without viral rebound. These results agree with an existing study using virologic failure as the end point,6 which noted that the time to virologic failure, defined as the first of 2 successive viral load measurements above 200 copies per milliliter after 16 weeks, was not significantly longer in the 4-drug arm. However, the particular advantages of the 4-drug regimen regarding time to initial suppression and rebound are seen more readily using the proposed approach.

In addition to providing an end point that is readily interpretable and simple to communicate, the proposed approach avoids several pitfalls associated with using virologic failure as an end point. For example, virologic failure is sometimes defined as the time to the first viral load measurement over 200 copies per milliliter at or after 16 weeks from randomization.5,6 Under this definition, the time to virologic failure is set to the ad hoc time point of 16 weeks if the patient fails to respond to treatment by achieving a suppressed viral load by that time. When the event of interest is virologic failure, the event pool is a mixture of 2 distinct types of events: patients who have experienced virologic suppression and then rebound and patients who did not achieve virologic suppression on or before the cut point. Such a composite end point fails to keep inferences distinct between these event types. For example, use of virologic failure as a composite end point hides differences in early suppression dynamics between treatment arms. Similarly, differences in the time to suppression are hidden if the time to virologic failure is estimated as the time from suppression to rebound only among patients who suppress.

The approach to measuring viral suppression illustrated here is based on the probability of being suppressed over time using ideas from multistate models developed for multiple time-to-event end points.10 As formalized by Gouskova et al,9 this approach can be extended to incorporate a time-varying weight to place greater importance on the probability of suppression at any time window during follow-up. For example, the weights can be used to improve precision by downweighting time points when the probability difference is highly variable (eg, by applying a weight of 1/standard error of the probability difference at each time point). Alternatively, weights can be used to tailor the analysis to research questions emphasizing outcomes at certain time windows. For example, if replication ceases at treatment initiation for both treatment arms, and the time to suppression is merely a function of the size and composition of a patient's viral reservoir,11–13 early differences in time spent in a state of suppression may be clinically less important than differences at later times. In this scenario, the investigator could downweight the differences in the probability of suppression at these early time points to focus the analysis on differences in the probability of suppression after some clinically relevant time point. When weights are set to 1 for all time points, as in the example presented here, the integral of the difference in the probability of suppression over time has the intuitive interpretation of the difference in the restricted mean number of days suppressed before rebound between treatment arms.

We have used this approach to compare the mean number of days spent in a state of suppression between arms of a randomized trial. This approach could also be used to compare suppression between exposure groups in observational studies using inverse probability weights14,15 or the parametric g-formula16,17 to account for confounding by measured variables. Extensions of this approach to observational studies would allow this end point to be used when examining the effects of exposures that are unlikely to be randomized. In addition, although we define a patient to be in a state of viral suppression after initial viral suppression and before the first viral rebound, this approach can be extended to allow for multiple cycles of suppression and rebound.

HIV-1 RNA viral load remains an important outcome measure in HIV randomized trials and observational studies. We have illustrated an end point that uses information on the time to viral suppression and time to subsequent viral rebound to provide a single summary measure of the mean time spent in a state of viral suppression before viral rebound in each treatment arm. This end point is well defined, has an appealing graphical representation, and facilitates straightforward comparisons of treatment effects between studies.

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Keywords:

viral load; virologic failure; viral suppression; HIV

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